On the direct insulator-quantum Hall transition in two-dimensional electron systems in the vicinity of nanoscaled scatterers
© Liang et al; licensee Springer. 2011
Received: 14 August 2010
Accepted: 11 February 2011
Published: 11 February 2011
A direct insulator-quantum Hall (I-QH) transition corresponds to a crossover/transition from the insulating regime to a high Landau level filling factor ν > 2 QH state. Such a transition has been attracting a great deal of both experimental and theoretical interests. In this study, we present three different two-dimensional electron systems (2DESs) which are in the vicinity of nanoscaled scatterers. All these three devices exhibit a direct I-QH transition, and the transport properties under different nanaoscaled scatterers are discussed.
The simultaneous presence of disorder and a strong enough magnetic field B can lead to a wide variety of interesting physical phenomena. For example, the integer quantum Hall effect is one of the most exciting effects in two-dimensional electron systems (2DES), in which the electrons are usually confined in layers of the nanoscale . In an integer quantum Hall (QH) state, the current is carried by the one-dimensional edge channels because of the localization effects. It has been shown that with sufficient amount of disorder, a 2DES can undergo a B-induced insulator to quantum Hall transition [2–5]. Experimental evidence for such an insulator-quantum Hall (I-QH) transition is an approximately temperature (T)-independent point in the measured longitudinal resistivity of a 2DES [3–5]. The I-QH transition continues to attract a great deal of interest both experimentally and theoretically as it may shed light on the fate of extended states [6–10], the true ground state of a non-interacting 2DES , and a possible metal-insulator transition in 2D [11, 12].
It is worth pointing out that in order to observe an I-QH transition separating the zero-field insulator from the QH liquid, one needs to deliberately introduce strong disorder within a 2DES. The reason for this is that the localization length needs to be shorter than the sample size. In the study by Jiang and co-workers , a 2DES without a spacer layer in which strong Coulomb scattering exists was used. Wang et al. utilized a 30-nm-thick heavily doped GaAs layer so as to allow the positively charged Si atoms to introduce long-range random potential in the 2DES . Hughes et al. have shown that when a Si-doped plane was incorporated into a 550-nm-thick GaAs film, a deep potential well can form in which the 2DES is confined close to the ionized donors and is therefore highly disordered . It has been shown that by deliberately introducing nanoscaled InAs quantum dots  in the vicinity of a modulation-doped GaAs/AlGaAs heterostructure, a strongly disordered 2DES which shows an I-QH transition can be experimentally realized [14, 15].
The transition/crossover from an insulator to a QH state of the filling factor ν > 2 in an ideal spinless 2DES can be denoted as the direct I-QH transition [16–19]. Such a transition has been attracting a great deal of interest and remains an unsettled issue. Experimental [16–19] and theoretical results [9, 10] suggest that such a direct transition can occur, and it is a quantum phase transition. However, Huckestein  has argued that such a direct transition is not a quantum phase transition, but a narrow crossover in B due to weak localization to Landau quantization.
In this study, the authors compare three different electron systems containing nanoscaled scatterers which all show a direct I-QH transition. The first sample is a GaAs 2DES containing self-assembled nanoscaled InAs quantum dots [13, 14, 21–23].
The second one is a 2DES in a nominally undoped AlGaN/GaN heterostructure [24–33] grown on Si substrate [33, 34]. Such a GaN-based electron system can be affected by nanoscaled dislocation and impurities . Finally, experimental results on the third sample, a delta-doped GaAs/AlGaAs quantum well with additional modulation doping [36, 37], will be presented. All the experimental results on the three completely different samples show that the direct I-QH transition does not occur with the onset of strong localization due to Landau quantization [20, 38]. Therefore, in order to obtain a thorough understanding of the direct I-QH transition, further studies are required.
Results and discussions
It has been suggested that by converting the measured resistivities into longitudinal and Hall conductivities, it is possible to shed more light on the observed I-QH transition . Figure 6 shows such results at various temperatures. Interestingly, for B < 5 T, σ xy is nominally T independent. Such data are consistent with electron-electron interaction effects. Over the whole measurement range, σ xx decreases with increasing T, consistent with electron-electron interaction effects. Unlike σ xy , σ xx shows a significant T dependence.
In conclusion, the authors have presented studies on three completely different electron systems. In these three samples, the nanoscaled scatterers, in close proximity of the 2DES, provide necessary disorder for observing the direct I-QH transition. In these studies, it has been shown that the crossover from localization to Landau quantization actually covers a wide range of magnetic field. Moreover, the observed direct I-QH transition is not necessarily linked with Landau quantization as no resistance oscillations are observed even up to a magnetic field 4 T higher than the crossing field. Most importantly, the onset of strong localization which gives rise to the formation of quantum Hall state does not correspond to the direct I-QH transition. All these three pieces of experimental evidence show that a 2DES in the vicinity of nanoscaled scatterers is an ideal playground for studying the direct I-QH transition. Furthermore, in order to obtain a thorough understanding of the underlying physics of the direct I-QH transition, modifications of Huckestein's model  must be made.
two-dimensional electron systems.
This research was supported by the WCU (World Class University) program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (Grant No. R32-2008-000-10204-0). C.T.L. acknowledges financial support from the NSC (Grant no: NSC 99-2119-M-002-018-MY3). The authors would like to thank Yi-Chun Su and Jau-Yang Wu for providing help in the experiments.
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